On the resolution of 3-dimensional terminal singularities (Q2387832)

Terminal singularities arise naturally in the theory of minimal models. Their analytic type is classified (works of Ried, Mori, Kollár, Shepard-Barron) in dimension 3. The paper under review studies the resolutions, some birational and combinatorial properties of 3-dimensional terminal singularities of type cD. It is shown that there is at most one non-rational exceptional divisor with discrepancy 1. Moreover, if such a divisor exists then it is birationally isomorphic to the product of the projective line with a hyperelliptic curve.